Method for determining the combustion ratio of a reciprocating-piston internal combustion engine

ABSTRACT

A method of determining a combustion air ratio of a reciprocating-piston internal combustion engine includes the steps of measuring a gradient of a combustion chamber pressure as a function of a position of a piston in a piston cylinder, for at least one operating cycle of the engine. Measured signals are formed representing the gradient of the combustion chamber pressure. The measured signals are digitized and entered into a programmed evaluation unit, where they are evaluated on the premise that energy prior to combustion and energy following or toward the end of combustion are at least approximately equal. Further, they are evaluated based on the equation ##EQU1## A value of the combustion air ratio is calculated from the evaluated digitized measured signals in an iterative computation process, and the value is displayed.

BACKGROUND OF THE INVENTION

The invention relates to a method of determining the combustion airratio λ (which is the ratio of the quantity of air supplied, to theminimum quantity of air required for the combustion of one unit ofquantity of fuel) of a reciprocating-piston internal combustion engine,particularly an Otto engine.

The methods used at this time to determine the combustion air ratio λ inreciprocating-piston internal combustion engines are based on thedetermination of the air mass, and the fuel mass, or an evaluation ofthe chemical composition of the exhaust gas. The disadvantage of thesemethods is that an exact determination of the combustion air ratiocannot be performed for individual operating cycles, particularly athigher engine rpms. In measurement processes employing a so-calledleanness sensor, the problem arises of the considerable temperaturedependency of this type of sensor, which leads to erroneous measurementswithout extensive temperature compensation. Moreover, with the aid of alambda sensor measurement or leanness sensor measurement, ultimatelyonly averaged values can be detected which may still be sufficient forthe regulations and/or controls of the fuel supply system of an internalcombustion engine. With the aid of a lambda sensor measurement orleanness sensor measurement, however, it is possible to make moreprecise statements about the operating-cycle-specific combustion airratio as a function of the combustion process, which is necessary inparticular for the optimization of aggregates as a whole, i.e.,reciprocating-piston internal combustion engines, including theaggregates needed for regulation and control.

SUMMARY OF THE INVENTION

The object of the invention is to create a method that permits thedetermination of the combustion air ratio λ for individual operatingcycles.

In the method of the invention, the gradient of the combustion chamberpressure is measured, as a function of the position of the piston in thecylinder, for at least one operating cycle, and the measured signalsthat represent the gradient of the combustion chamber pressure aredigitized, and the digitized measured signals are entered into aprogrammed evaluation unit in which the value of the combustion airratio is calculated from the measured gradient of the combustion chamberpressure in an iterative computational process, and the result ofcalculation is outputted. The basis of evaluation in the evaluation unitis the rule that the energy prior to combustion and the energy followingor toward the end of combustion are identical, or at least nearlyidentical.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates two graphical curves of an equation utilized by thepresent invention.

FIG. 2 is a graphical representation of a typical dependency of thecourse of a combustion function on the combustion air ratio.

FIG. 3 is a graphical representation of individual, typical operatingcycles in which the average combustion ratio is varied.

DETAILED DESCRIPTION OF THE INVENTION

Evaluation preferably takes place based on the following equation:##EQU2##

In a useful embodiment, at least one distinction parameter, particularlythe distinction parameter of "rich/lean," is additionally entered intothe evaluation unit in order to eliminate ambiguity. It is especiallyadvantageous when at least one distinction parameter derived from themeasurement of the gradient of the combustion chamber pressure isentered into the evaluation unit.

The method of the invention permits the determination of the combustionair ratio λ, independently of the rpm of the engine, for individualoperating cycles. An assumption of the invention is that, by means ofcombustion, the chemical energy level of the gas mixture in the cylinderdecreases, and the energy is released as change-in-volume work and wallheat. This conservation of energy is described by Equation 1.1 for thephase from the time of ignition to the end of combustion, where

    ______________________________________                                        u.sub.BreEnd                                                                          specific energy at end of combustion                                                                  [J/kg]                                        m       gas mass in combustion chamber at end                                                                 [kg]                                                  of combustion                                                         U.sub.ZZP                                                                             energy at time of ignition                                                                            [J]                                           p       pressure in combustion chamber                                                                        [N/m.sup.2 ]                                  dV      change in volume of combustion chamber                                                                [m.sup.3 ]                                    dQ.sub.Wand                                                                           wall heat               [J]                                           h       specific enthalpy of gas                                                                              [J/kg]                                        dm.sub.Blowby                                                                         leakage mass flowing past piston                                                                      [kg]                                          ______________________________________                                    

Practical tests have shown that one can assume as a prerequisite thatthe mixture combusts completely until the outlet valve opens. It can befurther assumed that the gas mixture is homogeneous at the end ofcombustion, that is, the time at which the outlet valve opens.

Because the engine is known with respect to its dimensions, particularlyregarding volume, the gas mass can be determined by a calculation of acharge change. Because the pressure at the end of combustion, that is,the time "outlet opens," is present as a measured value, the specificinternal energy U_(brEnd) Can be determined for this time as a functionof the combustion air ratio, which will be explained in detail below.

The internal energy at the time of ignition U_(ZZP) is only slightlydependent on λ. At the time of ignition, a known mixture of freshmixture and residual gas is present. Again, mass and pressure are known,so they can be determined as a function of λ.

The values considered to be a loss factor ##EQU3## are essentiallyformed by wall heat losses that can be used based on availableapproximation formulas, and also by the so-called leakage mass (Blowby), whose influence on the energy state is, however, so slight thatthis component can be disregarded.

Because U_(BreEnd), on the one hand, and U_(ZZP), on the other, arefunctions of the combustion air ratio λ, the following Equation 1.2 isto be solved in the evaluation unit: ##EQU4## This equation system to besolved is represented in FIG. 1. Curve 1 shows the right portion ofEquation 1.1, which is only slightly dependent on λ. Curve 2 shows theleft portion of Equation 1.1, i.e., the chemical equilibrium at thepressure at the end of combustion. From this it can be seen that the twopoints of intersection between curves 1 and 2 represent possiblesolutions of Equation 1.2.

Since it is improbable that the lambda sensor measurement will determinethe exact value, the evaluation unit is programmed so that itpredetermines a new λ value, and the calculation process is repeatedwith the new predetermined λ value until the result predetermined byEquation 1.1 or Equation 1.2, that is, the points of intersection ofcurves 1 and 2 in FIG. 1, has been reached. The λ value that has led tothe solution of the equation is then displayed.

The two solutions can also be found with the aid of a combustionfunction calculation, in which instance the combustion functionindicates the ratio of the combusted fuel mass to the entire fuel massused, with ##EQU5##

Because complete combustion is a prerequisite here, the combustionfunction must reach the value 1 at the end of combustion. The end valueof the combustion function is a function of λ. Again, the two solutionsof λ can be found iteratively.

As can be seen from FIG. 1, for an Otto engine, a solution results forboth a rich mixture (λ<1) and a lean mixture (λ>1). It is possible inprinciple to predetermine an additional measured value, for example themeasurement of the λ value, by way of a lambda sensor in order to selectthe correct solution. However, when rapid λ changes occur, a notinconsiderable danger of an erroneous solution is possible, because thesensor output signal cannot be allocated exactly to an operating cycle.

It is, however, particularly advisable to perform the method withoutadditional measured values, such as lambda sensor signals, in which casethe distinction parameter of rich/lean is likewise derived from themeasured pressure gradient per operating cycle. It has proven useful toenter into the evaluation unit at least one distinction parameterderived from the gradient of the combustion chamber pressure. Thefollowing parameters, which can be derived from the gradient of thecombustion chamber pressure, are considered as distinction parameters:the combustion delay, the length of combustion, the speed of combustionand the indicated average pressure.

The combustion delay is defined as the time between ignition and thefirst detectable increase in pressure due to combustion. The point ofthis pressure increase can be determined through calculation andevaluation of a combustion function. Because the pressure gradient canbe afflicted with small interferences, small fluctuations can occur inthe combustion function. Therefore, in determining the combustion delay,it is advisable to select the point at which a threshold value greaterthan the fluctuation is exceeded. In most instances, the 2- or5-percentage point of the combustion function is selected.

The length of combustion indicates the period between the time ofignition and the end of combustion. Determination of the end ofcombustion can be effected analogously to the determination of thebeginning of combustion, i.e., the point at which a threshold value ofthe combustion function is exceeded is determined (e.g. 95%, 98%). It isalso conceivable to determine the point as of which the combustionfunction no longer changes, or reaches its maximum value. The effectivelength of combustion is defined as the time between the beginning andend of combustion.

The typical dependency of the course of the combustion function on thecombustion air ratio is shown in FIG. 2. With increasing leanness, thecombustion delay and effective length of combustion increase.

The combustion speed is defined as the following: ##EQU6##

    ______________________________________                                        m        total mass           [kg]                                            s.sub.Bre                                                                              combustion speed     [m/sec]                                         χ.sub.Bre                                                                          derivation of combustion function                                                                  [1/sec]                                                  according to time                                                    ρ.sub.1                                                                            density of zone 1    [kg/m.sup.3 ]                                   A.sub.Flamfr                                                                           surface of flame front                                                                             [m.sup.2 ]                                               derivation of masses in zone 2                                       m.sub.2  according to time    [kg/sec]                                        ______________________________________                                    

Equation 1.3 is proposed for calculating a characteristic value from thecourse of the combustion speed. With this equation, the combustion speedis weighted with the mass conversion, which reduces the influence of thelocal λ non-homogeneity. ##EQU7##

The unit of this weighted combustion speed is (m/sec). Afterdetermination of the value S_(Bre),soch, in stoichiometric combustion ofaveraged pressure gradients, it can be assessed whether a rich or leancycle is present.

S_(Bre) >S_(Brestoch) rich

S_(Bre) <S_(Brestoch) lean

The known tendency of richer operation to lead to higher combustionspeeds can clearly be seen in a comparison of pressure gradients thatwere respectively averaged over 100 operating cycles, and in which theaverage combustion ratio was varied. FIG. 3 shows this connection forindividual, typical operating cycles. Attempts to apply this statementgenerally to individual operating cycles often lead to contradictions.

Because of these contradictions, the combustion speed course obtainedfrom the pressure gradient cannot be used in principle as the solecriterion for the rich/lean decision in individual cycles.

The indicated average pressure represents the change-in-volume work ofan operating cycle related to the stroke volume: ##EQU8##

The energy analysis shows that the combustion energy made available bythe fresh mixture has its maximum fairly precisely in the stoichiometricair ratio. Despite this, the output of an engine can be increased whenthe mixture is enriched, that is, if driving takes place when λ is lessthan 1. This phenomenon can be attributed to two effects. First, in anOtto engine, more intense cooling is effected by the greater fuelvaporization of the fresh mixture. Thus, more fresh mixture mass travelsinto the cylinder per operating cycle. Secondly, the high-pressureprocess is also influenced, which can be explained by a processcalculation and analysis. In a comparison of the combustion functioncourse of a rich operating cycle with that of a stoichiometric operatingcycle, it can be seen that more rapid combustion takes place in the richoperating cycle. The comparison processes will be examined here in orderto explain how shorter combustion can effect the output work. If thethermal losses are disregarded, an abrupt combustion at upper (top) deadcenter corresponds to the constant volume cycle. Constant-pressurecombustion, for example, can be realized through a controlled, slowercombustion. An increasingly faster combustion consequently more and moreclosely approaches the constant volume cycle, which represents the mostthermodynamically favorable process. For performing an adiabaticprocess, more work is performed with faster combustion and uniformenergy supply. These explanations for the adiabatic process also applyanalogously for the process with heat transfer.

To summarize, it can be stressed that, on the average, a richeroperating cycle leads to faster combustion and thus to a higherindicated average pressure P_(mi). The measurements were able tocorroborate this effect. In individual operating cycles, however, thecyclical fluctuations of other influential variables become morenoticeable, which impedes a reliable rich/lean decision based on P_(mi).

The above remarks show that the disclosed criteria for the rich/leandecision can lead to the correct rich/lean decision, but have a veryhigh error quota when applied individually. Therefore, it is advisableto use the individual criteria in combination in order to obtain areliable overall criterion.

If the evaluation unit is provided with a so-called fuzzy logic, theindividual criteria discussed above, namely combustion delay, length ofcombustion, indicated average pressure and combustion speed, can be usedas so-called fuzzy variables. The rich/lean decision can be made basedon the combination of fuzzy variables, because the individual criteriaare interfered with in different ways by the cyclical fluctuations ofother influential variables, so the combined criterion is more reliablethan the respective individual criteria.

The determination of the specific energy U_(ZZP) and U_(BreEnd) is knownin principle, but the way in which it can be used in programming theevaluation unit is reiterated in a summarizing representation below.Equations (5) and (31) show the internal energy U_(BreEnd), on the onehand, and U_(ZZP), on the other, as a function of λ. The determinationcan, however, also take place with the use of approximation formulas inorder to achieve speed-related advantages.

The above-described measuring method for deriving the combustion airratio λ from the measured gradient of the combustion chamber pressureresults in the possibility of determining the combustion air ratio λ foran individual operating cycle. In corresponding storage of the measuredvalues of a plurality of temporally successive operating cycles, inwhich the measured values of a plurality of directly consecutiveoperating cycles can be measured and stored and subsequently evaluatedsuccessively, it is possible not only to determine the combustion airratio λ for the different, stationary operating states, but also todetermine dynamic operating states, for example even in accelerations ordelays. Since no additional outlay for measuring technology is necessaryin engine test stands that are already equipped with the indicatingapparatuses for measuring the pressure gradient as a function of thepiston position, the method of the invention represents a good option ofinvestigating the influences of the peripheral aggregates in apredetermined engine construction, for instance the influences of theindividual components of mixture preparation, such as geometry and/ortemperature conditions in the intake conduit, nozzle arrangement, nozzleshape, etc. Because the determined value of the combustion air ratio,including the distinction criteria for the evaluation unit, is derivedfrom the gradient of the combustion chamber pressure during oneoperating cycle, the possibility essentially exists of also using thedetermined value of the combustion air ratio as a setting signal forcontrol or regulation in the region of the fuel supply of the engine.

For determining the specific energy at the time of ignition and the endof combustion, the following calculations are to be performed with agiven λ value and a known fuel composition; the result of thesecalculations is then entered into the evaluation unit as the basis forthe calculation process according to Equations 1.1 and 1.2, so that,starting at the measured pressure gradient, the measurement ordetermination of the λ value can be effected for one operating cycle.

In addition to the use for developmental work λ on the engine, this typeof control or regulation can be used in mass-produced automobiles.Hence, unlike in conventional λ regulation, a very quick λ reaction to achange in λ takes place, for example particularly in unstable operation.To achieve the highest possible utilization of the catalytic converter,the individual cycles are not necessarily pilot-controlled; rather, thehistory is taken into consideration and an integral value of λ=1 issought (storage effect of the catalytic converter).

A further improvement in the λ value of individual cycles can beachieved when the actual λ value of an operating cycle, or the deviationfrom the pilot control value, is registered (=stored) as a function ofthe respective operating state (e.g. characterized by rpm, load and/ordynamic parameters). When this operating state recurs, the associatedregistered value of the λ deviation in pilot control can be taken intoconsideration. A qualitatively high-value pilot control can be achievedwith this adaptive method.

Disclosed below is an option of determining the energy necessary forevaluation at the time of ignition and the end of combustion.

PROCEDURE FOR DETERMINING THE SPECIFIC ENERGY AT THE TIME OF IGNITIONAND THE END OF COMBUSTION

1. Determination of the fuel composition: ##EQU9##

2. Determination of the gas constant:

    R=Σσ.sub.i ·R.sub.m                   (2)

3. Determination of the temperature: ##EQU10##

4. Determination of the specific energy:

    u=Σσ.sub.i ·h.sub.m.sbsb.i.sup.° (T)-R·T                                          (4)

h_(m).sbsb.1.sup.° (T): present as a table for each fuel constituent

1. Determination of the material composition

The material composition of a mixture is described unambiguously by thespecific quantities σ_(i) of the individual constituents i. Thefollowing constituents i are taken into consideration: CO₂, CO, H₂ O,O₂, N₂, H₂ and fuel.

1.1 Composition of the gas at the end of combustion as a function of λ

To determine the exhaust gas composition, the fresh mixture, includingthe fuel, is formally divided into the constituents C, H₂, N₂, O₂ and H₂O. In a diesel engine, fuel must additionally be considered as theinitial fuel composition for the reaction. Therefore, no distinctionexists between a diesel engine and an Otto engine. Since the fuel wasformally divided into its constituents, this initial fuel compositioncannot be used to calculate energies or enthalpies of the mixture. As adistinction from the fresh mixture, the index "1" is used below insteadof "FG." The combustion products are assigned the index "2," and can beused to calculate the mixture enthalpy and energy. The mass remainsconstant during combustion, that is, m_(i) is equal to m₂. The Blow-Bylosses are insignificant for the observation of the chemicalcomposition. ##EQU11##

    ______________________________________                                        c       mass proportion of carbon in fuel                                                                   [--]                                            h       mass proportion of hydrogen in fuel                                                                 [--]                                            o       mass proportion of oxygen in fuel                                                                   [--]                                            m.sub.FL                                                                              mass of moist air     [kg]                                            M.sub.i mol mass of constituent i                                                                           [kg/mol]                                        χ.sub.H2O                                                                         mass proportion of water in air                                                                     [--]                                            L.sub.ST                                                                              stoichiometric combustion air ratio                                                                 [--]                                            m.sub.Br                                                                              fuel mass             [kg]                                            ______________________________________                                         ##EQU12##

In formulas 7 and 11, the mass proportions of the nitrogen and oxygen indry air are assumed to be ξ_(N2) =0.7671 and ξ_(o2) =0.2329. The basematerial balance states that the number of molecules of a base materialremains constant in a chemical reaction. Since the mass likewise remainsconstant, the specific quantities must also remain constant. It hasproven useful to make the following three case distinctions to calculatethe composition:

1.1a) Combustion air ratio λ≧1

For the sake of simplicity, it is assumed for this case that no carbonmonoxide is present in the combustion product. ##STR1## Base materialbalance

    C: σ.sub.2,CO.sbsb.2 =σ.sub.1,C                (12)

    H: σ.sub.2,H.sbsb.2.sub.O =σ.sub.1,H.sbsb.2.sub.O +σ.sub.1,H.sbsb.2                                   (13)

    N: σ.sub.2,N.sbsb.2 =σ.sub.1,N.sbsb.2          (14)

    O: σ.sub.2,O.sbsb.2 =σ.sub.1,O.sbsb.2 -σ.sub.1,C -1/2·σ.sub.1,H.sbsb.2                      (15)

1.1b) Combustion air ratio λ<1 and fuel containing a proportion of C##STR2## For a fresh gas mix having a fuel that contains C and in whichλ<1, the water-gas equilibrium is assumed in order to obtain, inaddition to the four base material balance equations, a further equationfor the fifth constituent of the exhaust gas. This equilibrium constantis only dependent on the temperature of the mixture. ##EQU13##

For the exhaust gas composition, the equilibrium constant is usually setat 1750K (transformation temperature)

    K(1750)=0.2773

The solution of the equation system leads to the following solution forthe specific quantities of the combusted substance: ##EQU14##

    σ.sub.2,N.sbsb.2 =σ.sub.1,N.sbsb.2             (20)

    σ.sub.2,H.sbsb.2 =σ.sub.1,H.sbsb.2 -σ.sub.2,H.sbsb.2.sub.O +σ.sub.1,H.sbsb.2.sub.O(21)

    σ.sub.2,CO.sbsb.2 =2σ.sub.1,O.sbsb.2 -σ.sub.2,H.sbsb.2.sub.O -σ.sub.1,C +σ.sub.1,H.sbsb.2.sub.O                             (22)

    σ.sub.2,CO =σ.sub.1,C -σ.sub.2,CO.sbsb.2 (23)

1.1.c) Fuel without a proportion of C

This case applies to, for example, pure hydrogen combustion. ##STR3##

    σ.sub.2,N.sbsb.2 =σ.sub.1,N.sbsb.2             (24)

The following equations apply for λ≧1:

    σ.sub.2,H.sbsb.2.sub.O =σ.sub.1,H.sbsb.2.sub.O +σ.sub.1,H.sbsb.2                                   (25)

    σ.sub.2,O.sbsb.2 =σ.sub.1,O.sbsb.2 -1/2·σ.sub.1,H.sbsb.2                      (26)

    σ.sub.2,H.sbsb.2 =0                                  (27)

The following equations apply for λ<1:

    σ.sub.2,H.sbsb.2.sub.O =2σ.sub.1,O.sbsb.2 +σ.sub.1,H.sbsb.2.sub.O                             (28)

    σ.sub.2,H.sbsb.2 =σ.sub.1,H.sbsb.2 -2σ.sub.1,O.sbsb.2(29)

    σ.sub.2,O.sbsb.2 =0                                  (30)

1.2 Composition during compression

In a diesel engine, the mixture comprises moist air and residual gasduring the compression phase, whereas the mixture of the Otto engineadditionally contains fuel.

    ______________________________________                                        m.sub.FL                                                                              mass of moist air     [kg]                                            m.sub.FG                                                                              mass of fresh mixture [kg]                                            σ.sub.FG,i                                                                      specific material quantity of the                                                                   [kmol/kg]                                               constituent i in the fresh mixture                                    M.sub.i mol mass of the constituent i                                                                       [kg/kmol]                                       χ.sub.H2O                                                                         mass proportion of water in the air                                                                 [--]                                            L.sub.ST                                                                              stoichiometric combustion air ratio                                                                 [--]                                            ______________________________________                                         ##EQU15##

In formulas 33 and 34, the mass proportions of nitrogen and oxygen,##EQU16## are assumed to be ξ_(N2) =0.7671 and ξ_(o2) =0.2329 in dryair. ##EQU17##

The remaining specific material quantities of CO₂, H₂ and CO are zero inthe fresh mixture. During the compression phase, the mixture comprises afresh mixture and residual gas. The specific material quantities of themixture constituents during the compression phase are calculatedaccording to formula 36:

    σ.sub.Kompr.,i =σ.sub.Fg,i ·(1-ξ.sub.RG)+σ.sub.2,i ·ξ.sub.RG(36) ##STR4##

I claim:
 1. A method of determining a combustion air ratio of a reciprocating-piston internal combustion engine, comprising the steps of: measuring a gradient of a combustion chamber pressure as a function of a position of a piston in a piston cylinder, for at least one operating cycle of the engine;forming measured signals representing the gradient of the combustion chamber pressure; digitizing the measured signals; entering the digitized measured signal into a programmed evaluation unit; evaluating the digitized measured signals in the programmed evaluation unit on the premise that energy prior to combustion and energy following or toward the end of combustion are at least approximately equal, and based on the equation ##EQU18## calculating a value of the combustion air ratio from the evaluated digitized measured signals in an iterative computation process; and displaying the value.
 2. The method defined in claim 1, wherein the engine is an Otto engine.
 3. The method defined in claim 1, wherein said entering step further includes entering at least one distinction parameter into the evaluation unit in order to eliminate ambiguity.
 4. The method defined in claim 3, wherein the distinction parameter is a "rich/lean" distinction parameter.
 5. The method defined in claim 1, wherein said entering step further includes entering at least one distinction parameter derived from said measuring step into the evaluation unit.
 6. The method defined in claim 1, wherein said measuring step includes measuring the gradient of the combustion chamber pressure of a plurality of temporally successive operating cycles; further comprising the step of storing the measured gradients; and wherein said evaluating step includes successively evaluating the stored measured gradients.
 7. The method defined in claim 1, further comprising the step of using the value of the combustion air ratio as a setting signal for control or regulation in a region of a fuel supply of the engine.
 8. The method defined in claim 7, further comprising the step of storing the value of the combustion air ratio or a deviation from a nominal value of the combustion air ratio, together with an operating state of the engine; and, when the operating state recurs, evaluating the stored value for corrective purposes in pilot control. 